Chapter 14

The Ideal Gas Law

and

Kinetic Theory

HydrogenOxygen Carbon

Sodium

Every element has an atomic mass

(1 u = 1.6605 x 10-27 kg)

Measured in atomic mass units (u)

………

Molecules – combinations of atoms

Ex: Water 2 Hydrogens

1 OxygenH2O

= 2 (1.00794 u) + 1 (15.9994 u)

Molecular mass = 2 (mH) + 1 (mO)

= 18.0153 u

Objects contain billions of particles

1 mole of particles = 6.022 x 1023 particles = NA

Avogadro’s Number

Ex: Calculate the mass in grams of 1 mole of hydrogen atoms.

(The SI unit for quantity of a substance)

One mole of a substance

has the same mass in grams (g)

that one particle has in

atomic mass units (u).

The Ideal Gas Law

Web Link: Ideal Gas

PV=nRT

P = Pressure

V = Volume

n = # of moles

R = 8.31 J/mol K

T = Temp. (Kelvins)If N = # of particles

PV=NkT

k = Boltzmann’s Constant = 1.38 x 10-23 J/K = R/NA

Ideal Gas at Constant Temperature

Isothermic

PV=nRT

constant

PV=constant

PiVi= PfVf

or Boyle’s Law

Since Pressure and Volume are inversely proportional:

P

V

Ideal Gas at Constant Pressure

PV=nRT

constant

VT

nRP

VT

constant

VT

V

Ti

i

f

f

or Charles’ Law

Use the ideal gas law to decide which answer best reflects the number of moles of particles in an

automobile tire:

a) .0025 mol b) .025 mol c) 2.5 mol d) 2500 mol

We haven’t yet calculated the speeds of the molecules in an ideal gas……

Web Link: Gas Temperature

Ideal Gas

This molecule has an average speed

This one has a different average speed

Distribution Curve:

What about the Kinetic Energy of a gas molecule?

m

vKE = ½mv2

What about the average Kinetic Energy of a group of gas molecules?

KE = ½mvrms2

Recall: Higher temperature

Greater average molecule speed

More Kinetic Energy KE Temp

K E kT32 Average KE of an

ideal gas molecule

(k = Boltzmann’s constant = 1.38 x 10-23 J/K)

Kelvin temperature

12 rm s

2 32m v kT

So now we can relate the mass, speed, and temperature of molecules in an ideal gas:

A single molecule has no temperature since temperature is an averaging effect.

Temperature is simply a measure of the average Kinetic Energy of the molecules of a substance.

Notes:

Web Link: Molecules in Motion

Two containers of different ideal gases have the same temperature. Do the molecules of both gases

have the same vrms ?

A. Yes B. No

Internal Energy (U) – the sum of all types of energies of the molecules of a substance

For a Monatomic Ideal Gas:

one-atom

U = (# atoms)(½mvrms2)

Why isn’t this true for a Diatomic (2-atom)gas?

Web Link: Diatomic Molecule

U nRT32

Internal Energy of n moles of a monatomic, ideal gas at temp T

(Example:Neon)

(U T for any ideal gas)

Diffusion – when molecules move from a region of higher concentration to a region of lower concentration

perfume in air

Solute – the substance that is diffusing

Solvent – what it’s diffusing into

Web Link: Diffusion

Examples:

cream in coffee

Web Link: Brownian Motion

Remember heat conduction?

The equation for diffusion is similar. Just replace the conduction quantities with the diffusion quantities:

A

L

Q mass (m)

Qk A T t

L

m

D A C t

L

Fick’s Law of Diffusion

T concentration diff. (C)

k diffusion constant (D)

Chapter 15

Thermodynamics

Thermodynamics

Heat (Q) Chapters 12,13,14

Work (W) Chapter 6

Ex:

Rub hands together

W Q

Car engine

Q W

Ex:

SurroundingsSystem

Walls can be either:

Diathermal - heat can flow through

or Adiabatic – heat can’t flow through

In Thermodynamics we talk about the state of the system:

Pressure, Volume & Temperature

4 Laws of Thermodynamics(0th, 1st, 2nd, 3rd)

0th Law of Thermodynamics

Consider 3 objects and their temperatures:

T1 T2 T3

If T1 = T2 and T2 = T3

then T1 = T3

Duuuu

Recall:

Forces do Work (W)

Can change Kinetic Energy (KE)

Can change Potential Energy (PE)

Heat (Q)Can change

Internal Energy (U)

also

In any of the above cases,

Total Energy is conserved

which brings us to…………

1st Law of Thermodynamics

U = Uf – Ui = Q - W

U = Change in internal energy of a system

Q = Heat added to the system

W = Work done by the system

- (Work done on the system)

Ex:

a) If 600 J of heat is added to a system as 200 Joules of work is done on the system, what is the change in its internal energy?

b) If 300 J of heat is added to a system as 300 joules of work is done by the system, what is the change in its internal energy?

Ex: A monatomic, ideal gas

3 moles

If the temperature is raised by 200 K while 5000 Joules of heat is added, find

the work done on the gas.

A. -2500 J

B.+2500 J

C. -7500 J

D.+7500 J